Ah, now in my old role-playing circles that was a common question. Ars Magica calls it a heart-beast, which I think is a much more poetic term. We used to say you couldn't name your own heart-beast, it had to be an animal suggested for you by a friend, and if you didn't dismiss it as preposterous, but instead liked it, and agreed with it, however unlikely the animal - well, then it was your heart-beast!

Mine was a vulture. They are nature's vacuum cleaners, you know. I am therefore unreasonably fond of them as a result :)